Abstract

We show a special effect of localization in the temporal frequency domain of light pulses that propagate in a dispersive single-mode fiber in the presence of a time-periodic phase modulation that is repeatedly applied at equally spaced locations along the fiber. The effect is analogous to the dynamical localization that occurs for the quantum kicked rotor, which is similar to Anderson localization in disordered solids. The wave behavior eliminates the diffusive spread of sidebands (harmonics). The light propagation, which is described by a Schrödinger-like propagation equation, can provide a new testing ground for the investigation of localization besides shedding light on technologically important pulse propagation in fibers and mode-locked lasers.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982); D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984).
    [CrossRef]
  2. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
    [CrossRef]
  3. For reviews see D. J. Thouless, in Critical Phenomena, Random Systems, and Gauge Theories, K. Osterwalder and R. Stora, eds., proceedings of the Les-Houches Summer School (North-Holland, Amsterdam, 1986), p. 681; I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).
  4. F. Haake, Quantum Signatures of Chaos (Springer, New York, 1991).
  5. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
    [CrossRef]
  6. J. Krug, Phys. Rev. Lett. 59, 2133 (1987).
    [CrossRef] [PubMed]
  7. R. E. Prange and S. Fishman, Phys. Rev. Lett. 63, 704 (1989); O. Agam, S. Fishman, and R. E. Prange, Phys. Rev. A 45, 6773 (1992).
    [CrossRef] [PubMed]
  8. F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
    [CrossRef] [PubMed]
  9. B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998); H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
    [CrossRef]
  10. B. Fischer, A. Rosen, A. Bekker, and S. Fishman are preparing a paper entitled “Experimental observation of localization in the spatial frequency domain of a kicked optical system.”
  11. G. P. AgrawalNonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

1998 (1)

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998); H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
[CrossRef]

1995 (1)

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

1989 (1)

R. E. Prange and S. Fishman, Phys. Rev. Lett. 63, 704 (1989); O. Agam, S. Fishman, and R. E. Prange, Phys. Rev. A 45, 6773 (1992).
[CrossRef] [PubMed]

1987 (1)

J. Krug, Phys. Rev. Lett. 59, 2133 (1987).
[CrossRef] [PubMed]

1982 (1)

S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982); D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984).
[CrossRef]

1958 (1)

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Agrawal, G. P.

G. P. AgrawalNonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

Anderson, P. W.

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Barucha, C. F.

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

Bekker, A.

B. Fischer, A. Rosen, A. Bekker, and S. Fishman are preparing a paper entitled “Experimental observation of localization in the spatial frequency domain of a kicked optical system.”

Fischer, B.

B. Fischer, A. Rosen, A. Bekker, and S. Fishman are preparing a paper entitled “Experimental observation of localization in the spatial frequency domain of a kicked optical system.”

Fishman, S.

R. E. Prange and S. Fishman, Phys. Rev. Lett. 63, 704 (1989); O. Agam, S. Fishman, and R. E. Prange, Phys. Rev. A 45, 6773 (1992).
[CrossRef] [PubMed]

S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982); D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984).
[CrossRef]

B. Fischer, A. Rosen, A. Bekker, and S. Fishman are preparing a paper entitled “Experimental observation of localization in the spatial frequency domain of a kicked optical system.”

Grempel, D. R.

S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982); D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984).
[CrossRef]

Gutzwiller, M. C.

M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
[CrossRef]

Haake, F.

F. Haake, Quantum Signatures of Chaos (Springer, New York, 1991).

Klappauf, B. G.

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998); H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
[CrossRef]

Krug, J.

J. Krug, Phys. Rev. Lett. 59, 2133 (1987).
[CrossRef] [PubMed]

Moore, F. L.

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

Oskay, W. H.

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998); H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
[CrossRef]

Prange, R. E.

R. E. Prange and S. Fishman, Phys. Rev. Lett. 63, 704 (1989); O. Agam, S. Fishman, and R. E. Prange, Phys. Rev. A 45, 6773 (1992).
[CrossRef] [PubMed]

S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982); D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984).
[CrossRef]

Raizen, M. G.

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998); H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
[CrossRef]

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

Robinson, J. C.

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

Rosen, A.

B. Fischer, A. Rosen, A. Bekker, and S. Fishman are preparing a paper entitled “Experimental observation of localization in the spatial frequency domain of a kicked optical system.”

Steck, D. A.

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998); H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
[CrossRef]

Sundaram, B.

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

Thouless, D. J.

For reviews see D. J. Thouless, in Critical Phenomena, Random Systems, and Gauge Theories, K. Osterwalder and R. Stora, eds., proceedings of the Les-Houches Summer School (North-Holland, Amsterdam, 1986), p. 681; I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

Phys. Rev. (1)

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Phys. Rev. Lett. (5)

J. Krug, Phys. Rev. Lett. 59, 2133 (1987).
[CrossRef] [PubMed]

R. E. Prange and S. Fishman, Phys. Rev. Lett. 63, 704 (1989); O. Agam, S. Fishman, and R. E. Prange, Phys. Rev. A 45, 6773 (1992).
[CrossRef] [PubMed]

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998); H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
[CrossRef]

S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982); D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984).
[CrossRef]

Other (5)

B. Fischer, A. Rosen, A. Bekker, and S. Fishman are preparing a paper entitled “Experimental observation of localization in the spatial frequency domain of a kicked optical system.”

G. P. AgrawalNonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

For reviews see D. J. Thouless, in Critical Phenomena, Random Systems, and Gauge Theories, K. Osterwalder and R. Stora, eds., proceedings of the Les-Houches Summer School (North-Holland, Amsterdam, 1986), p. 681; I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

F. Haake, Quantum Signatures of Chaos (Springer, New York, 1991).

M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Evolution of the frequency spectrum according to Eq. (1) (the sideband intensity I is on a 10-based logarithmic scale versus the number of sidebands, n), showing the convergence to the exponential profile as localization occurs. β2=20 ps2/km,κ=5,z0=40 km, and Ω/2π=8 GHz.

Fig. 2
Fig. 2

Route to localization, showing the frequency width according to Eq. (1) (standard deviation of n) as a function of the number of kicks, N, for (a), ordered system modulation and (b), diffusive behavior of the classical case, where we treat intensities rather than amplitudes or where the modulation phase of the kicks is random. β2=20 ps2/km,κ=5,z0=40 km, and Ω/2π=8 GHz.

Fig. 3
Fig. 3

Schematic of an experimental realization of the fiber kicked system in a loop configuration as repeated modulations and kicks are applied as a pulse circulates in the loop.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

iψz=β222ψT2+κ cosΩTNδz-Nz0ψ.

Metrics